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Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to ...

The geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex (Honsberger 1995, p. 120) is called the Steiner ...

The ordinary differential equation z^2y^('')+zy^'+(z^2-nu^2)y=(4(1/2z)^(nu+1))/(sqrt(pi)Gamma(nu+1/2)), where Gamma(z) is the gamma function (Abramowitz and Stegun 1972, p. ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

The biconnected graph theta_0 on seven nodes and seven edges illustrated above. It has chromatic polynomial pi_(theta_0)(z)=z^7-8z^6+28z^5-56z^4+68z^3-47z^2+14z and chromatic ...

Analytic representations the symmetric triangle wave with period 2 and varying between -1 and 1 include f(x) = 2/pisin^(-1)[sin(pix)] (1) = 1-2|1-[2(1/2x+1/4 (mod 1))]| (2) = ...

A series involving three sums. Examples of convergent triple series include sum_(i=1)^(infty)sum_(j=1)^(infty)sum_(k=1)^(infty)1/((ijk)^2) = 1/(216)pi^6 (1) ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...